Question

Evaluate the discriminant for the following equation. Then use it to determine the number of distinct​ solutions, and tell whether they are​ rational, irrational, or nonreal complex numbers. 5 x squared plus 11 x plus 6 equals 0

Answer 1

The Solutions are distinct and rational

Explanation:

Given the general form of a quadratic equation: ax²+bx+c=0

The discriminant D=b²-4ac is used to determine the nature of the roots of the quadratic equation.

There are three cases:

1. If b² - 4ac > 0

The quadratic equation has two real, distinct (different) roots.

2.If b² - 4ac < 0

The quadratic equation has no real roots. i.e. It has complex roots

3. If b² - 4ac = 0

The quadratic equation has two real, identical roots.

Given our equation:

5x²+11x+6=0

a=5, b=11, c=6

The discriminant:

D=b²-4ac=11²-4(5)(6)=1

Since D=1>0, the roots of the equation are real and distinct.